Method 1 is the most cost-effective. If labor costs double, Method 1 is still the best option.
To determine the best production method, we need to compare the total cost of each method. Method 1: 50 units of labor and 10 units of capital, Method 2: 20 units of labor and 40 units of capital, Method 3: 10 units of labor and 70 units of capital. The cost of labor is given as $100/unit and the cost of capital is $400/unit.
Method 1 cost = (50 x $100) + (10 x $400) = $5000 + $4000 = $9000. Method 2 cost = (20 x $100) + (40 x $400) = $2000 + $16000 = $18000. Method 3 cost = (10 x $100) + (70 x $400) = $1000 + $28000 = $29000.
Hence, the best production method is Method 1. If the cost of labor rises to $200/unit, the costs for each method will double. Therefore, Method 1 will still be the best production method as it will have the lowest cost at $18000.